2x^2-14-x=-x^2

Solution for 2x^2-14-x=-x^2 equation:

2x^2-14-x=-x^2

We move all terms to the left:

2x^2-14-x-(-x^2)=0

We add all the numbers together, and all the variables

2x^2-(-x^2)-1x-14=0

We get rid of parentheses

2x^2+x^2-1x-14=0

We add all the numbers together, and all the variables

3x^2-1x-14=0

a = 3; b = -1; c = -14;
Δ = b2-4ac
Δ = -12-4·3·(-14)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-13}{2*3}=\frac{-12}{6}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+13}{2*3}=\frac{14}{6}
=2+1/3
$